PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
90016^70974-13755229Lelio R Paula10/2012
90022^183446-11307355223Enzo Doria07/2014
90032^183441+57729457555222Lelio R Paula03/2013
90045^79000-655219Lelio R Paula10/2012
90052^183413-90155213Yves Minet01/2012
900619^43168-5055202Lelio R Paula02/2013
90072^183340+1968355191Lelio R Paula02/2012
90086^70923+3555189Lelio R Paula10/2012
90092^183317-403555184Lelio R Paula01/2011
90102^183284-1555174Lelio R Paula03/2011
90112^183255+14955166Lelio R Paula02/2011
90124*10^55165+8755166Robert Price05/2016
9013(3^115574+4)/6303755139Lelio R Paula03/2012
90142^183165-11233355139Enzo Doria06/2014
9015(109^27061-1)/10855133Richard Fischer09/2017
90162^183142+85555132Lelio R Paula01/2011
9017(49*10^55129+383)/955130Robert Price04/2017
90182^183019+25525555095Lelio R Paula01/2011
9019(10^55084-19)/955084Robert Price10/2017
90203*10^55077+755078Erik Branger11/2013
9021(62*10^55075-71)/955076Robert Price09/2015
902227499!2-3255070Robert Price10/2015
902315307^3958+3958^1530755067Hans Havermann08/2016
902470^29836-6955051Norbert Schneider10/2012
902518^43854-8355049Lelio R Paula02/2013
90267^65126+5855038Lelio R Paula10/2012
90272^182827-161555037Lelio R Paula11/2009
90287*10^55030-955031Dmitry Domanov11/2010
90292^182768-405555019Yves Minet02/2018
90306^70702+2355017Lelio R Paula10/2012
9031(23*2^182753+1)/15155014Lelio R Paula07/2012
90322^182743-161555012Lelio R Paula11/2009
9033(24737*2^182736+1)/39955011Lelio R Paula05/2014
90343^115280-956855003Enzo Doria02/2013
90352^182656-1284954985Enzo Doria10/2012
903612791^13388-13388^1279154984Norbert Schneider03/2018
90379*19^42995+1654981Curtis Bright05/2015
90382^182627+2842554977Lelio R Paula11/2009
90392^182597-11305354968Enzo Doria07/2014
9040(3^115213+2)/3090672554964Lelio R Paula03/2012
90412^182581-197554963Yves Minet09/2012
9042(2*10^54960-179)/354960Robert Price11/2017
904427449!!-1654959Robert Price06/2015
9043(22*10^54958-73)/354959Robert Price09/2017
90464^91283-3^9128354958Jean-Louis Charton01/2004
90452^182565+10754958Lelio R Paula11/2009
90472^182560+205354957Lelio R Paula12/2010
90482^182451-18245154924Henri Lifchitz10/2004
90492^182444+8154922Henri Lifchitz10/2005
90502^182433+7410554918Enzo Doria04/2016
905120^42206-524354912Enzo Doria03/2013
90522^182394+8554907Lelio R Paula02/2011
90532^182374-11228754901Enzo Doria06/2014
9054(47^32833-33^32833)/1454899Serge Batalov12/2016
90552^182363-11316754897Enzo Doria07/2014
90562^182359-11222154896Enzo Doria06/2014
9057(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
9058(17*2^182274+1)/146754869Lelio R Paula01/2012
905918^43698-554853Lelio R Paula02/2013
90602^182209-189354851Yves Minet09/2012
90612^182194-344354846Yves Minet12/2016
906215023^4468+4468^1502354836Hans Havermann08/2016
90632^182135+9014354829Yves Minet10/2010
90642^182119+7433354824Enzo Doria04/2016
906514289^6860+6860^1428954818Hans Havermann08/2016
90663^114892-114892^354818Norbert Schneider03/2017
90672^182070-4735554809Lelio R Paula01/2011
90683^114869+7654807Lelio R Paula10/2012
90698^60681-60681^854801Norbert Schneider12/2016
90701897^16710+16710^189754777Serge Batalov05/2014
9071Phi(61868,59)54776Enzo Doria04/2012
9072113^26679+254775Lelio R Paula05/2013
90733^114789-7454769Lelio R Paula10/2012
907415^46567+9854768Lelio R Paula02/2013
9075(2*10^54767-71)/354767Robert Price01/2017
9076(298*10^54765-7)/354767Robert Price06/2017
9077(21*2^181931-1)/16999754763Lelio R Paula01/2014
90782^181913+2954762Henri Lifchitz06/2005
9079(31*10^54761-121)/954762Robert Price06/2016
90802^181887+18954754Lelio R Paula02/2011
90812^181874+181874^2-154750Robert Price04/2014
9082(2^181865+9)/733954743Lelio R Paula02/2012
90835^78314-9254740Lelio R Paula10/2012
9084(163*10^54727-1)/954729Serge Batalov12/2014
908515^46531+7454725Lelio R Paula02/2013
9086277^22400-34854712Enzo Doria07/2012
90876^70302+10154706Lelio R Paula10/2012
90883^114622-1040854689Enzo Doria02/2013
9090(23*2^181674+1)/48954688Lelio R Paula01/2012
90892^181669-155154688Yves Minet08/2012
9091(57352^11491-1)/5735154676Serge Batalov04/2015
9092(31*2^181629-1)/1073472154671Lelio R Paula01/2014
9093(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
909413^49073+4654665Lelio R Paula01/2013
9095(57042^11491-1)/5704154649Serge Batalov04/2015
909720^42000+7354644Lelio R Paula02/2013
9096(67607*2^181517+1)/165554644Lelio R Paula05/2014
909833*10^54634+754636Robert Price07/2016
909920^41988+6154628Lelio R Paula01/2013
910020^41988-812354628Enzo Doria03/2013
91012^181420+2118154613Yves Minet03/2011
9102(19*10^54608+161)/954609Robert Price07/2016
910319^42696-2454598Lelio R Paula02/2013
9104(44*10^54596-503)/954597Robert Price10/2017
9105(74*10^54583+61)/954584Robert Price10/2015
91062^181316-9439554582Lelio R Paula09/2011
910714751^5006+5006^1475154572Hans Havermann08/2016
910814^47609+3954567Lelio R Paula02/2013
910912696^13295-13295^1269654559Norbert Schneider01/2018
9110(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
91123^114327-7454548Lelio R Paula10/2012
9111(44*10^54547-161)/954548Robert Price11/2017
9113gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
9114(17*10^54537-47)/354538Robert Price05/2017
91152^181155-1155*18115554534Henri Lifchitz02/2005
9116Phi(61672,83)54533Enzo Doria05/2012
9117(2*10^54527-197)/354527Robert Price11/2017
91189*2^181128+754526Lelio R Paula03/2014
911989*10^54518-754520Robert Price03/2017
91202^181090-11324754514Enzo Doria07/2014
912114031^7670+7670^1403154508Hans Havermann08/2016
912214210^6849+6849^1421054505Hans Havermann08/2016
91232^181043-19954500Lelio R Paula02/2011
912412^50499+554498Lelio R Paula01/2013
912512^50491+554489Lelio R Paula01/2013
91266^70016-14554484Lelio R Paula10/2012
912711^52313-960054479Enzo Doria02/2013
91282^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
91292^180946-11104154471Enzo Doria05/2014
9130(64*10^54467+287)/954468Robert Price04/2016
9131(32*10^54458+319)/954459Robert Price10/2017
91325^77907-2*3^7790754455Mike Oakes11/2009
913320^41853-562354453Enzo Doria03/2013
913414^47506-7554448Lelio R Paula02/2013
9135(25*10^54443-67)/354444Robert Price11/2017
91362^180839-11343754438Enzo Doria08/2014
91373^114085+2854433Lelio R Paula10/2012
9138Phi(141230,10)54432Ray Chandler08/2009
91396^69946-5554429Lelio R Paula10/2012
9140p(11796)#/2-102454427Robert Price09/2017
91415*2^180796+354426Lelio R Paula03/2014
9142(23*2^180782-1)/9154421Lelio R Paula01/2014
91439*6^69928-754416Lelio R Paula09/2014
914492^27701-91^2770154399Robert Price08/2015
9145(2^180687-3)*6-754393Gilbert Mozzo04/2016
9146(5*10^54388-11)/354389Erik Branger12/2013
914720^41799-304354382Enzo Doria03/2013
914813860^8387+8387^1386054382Hans Havermann08/2016
9149(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
91507^64329-1854365Lelio R Paula10/2012
91512^180551-96754352Yves Minet01/2012
915215^46209-7454347Lelio R Paula02/2013
915310^54345+2973954346Patrick De Geest08/2013
915410^54345-14138154345Patrick De Geest09/2013
9155lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
9156177^24171-254336Lelio R Paula10/2017
91572^180496+1554335Lelio R Paula02/2011
91581845^16636+16636^184554334Serge Batalov05/2014
915911^52169-7054329Lelio R Paula01/2013
91602^180446-403154320Yves Minet02/2018
916113693^9262+9262^1369354317Hans Havermann06/2016
91622^180429-11310154315Enzo Doria07/2014
91632^180423-11205154313Enzo Doria05/2014
916416112^2349+2349^1611254312Hans Havermann06/2016
9165(79^28621-1)/7854311Paul Bourdelais08/2017
9166(13^48751+4^48751)/1754305Robert Price05/2013
91672^180370+1291554297Lelio R Paula09/2012
9168(10^54290+41)/354290Robert Price01/2017
916915108^3917+3917^1510854283Hans Havermann06/2016
91702^180317-301954281Yves Minet10/2014
91712^180314+85554280Lelio R Paula10/2009
917219^42425+9454252Lelio R Paula02/2013
91732^180180-100544954240Paul Bourdelais11/2012
91742^180173-277354238Yves Minet07/2014
917513367^11418+11418^1336754238Hans Havermann06/2016
9176427^20614+20614^42754224Norbert Schneider06/2016
91772^180124-8795954223Gary Barnes08/2009
91782^180111-11310154219Enzo Doria07/2014
91792^180101-11487154216Enzo Doria05/2015
9180(11*2^180099+1)/5161754212Lelio R Paula07/2012
91822^180070+46554207Lelio R Paula09/2012
918113683^9154+9154^1368354207Hans Havermann06/2016
9183810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
91842^180014+61354190Jason Earls04/2008
91852^180007+10154188Lelio R Paula02/2011
91862^180001+4187754186Jim Fougeron08/2002
91872^180000+13015354186Jim Fougeron09/2002
91883^113565-7454185Lelio R Paula10/2012
918950^31891-4954182Norbert Schneider07/2014
9190(5*2^179991-1)/1142754180Lelio R Paula01/2014
91913^113548+2654177Lelio R Paula10/2012
9192(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
9193181^23996-254176Lelio R Paula10/2017
91944159^14969-13854173Enzo Doria07/2012
91962^179955+577554172Lelio R Paula10/2009
91952^179953-23131354172Enzo Doria05/2014
91975^77485+654160Lelio R Paula10/2012
919818^43141+8554154Lelio R Paula02/2013
919910^54149+18764754150Patrick De Geest07/2017
92023^113489-34054149Lelio R Paula10/2012
920010^54149-80000154149Robert Price06/2017
920110^54149-3650154149Patrick De Geest07/2017
92037^64070+9054146Lelio R Paula10/2012
920412549^13210-13210^1254954143Norbert Schneider12/2017
920518^43131+7154142Lelio R Paula02/2013
92062^179826-13154134Lelio R Paula02/2011
92072^179815-11273554130Enzo Doria06/2014
92082^179806+7384954127Enzo Doria04/2016
92092^179790+3354123Donovan Johnson02/2006
921014287^6138+6138^1428754120Hans Havermann06/2016
9211(17*10^54117+1)/954118Serge Batalov05/2010
92122^179763-18954115Lelio R Paula02/2011
9213(21181*2^179770+1)/302910554115Lelio R Paula05/2014
92141828^16589+16589^182854113Serge Batalov05/2014
921620^41588-588354108Enzo Doria03/2013
921550^31847-4954108Norbert Schneider07/2014
92172^179733-685554106Lelio R Paula10/2009
921820^41584-558354103Enzo Doria03/2013
921910^54084+3*3^5408454085Mike Oakes05/2010
92202^179613-179554069Lelio R Paula10/2009
92212^179589-101152354062Paul Bourdelais11/2012
92222^179574-253154058Yves Minet07/2014
9223(41*10^54051-23)/954052Robert Price05/2015
9224117^26131-11654044Norbert Schneider10/2013
9225(10^54038-31)/354038Serge Batalov12/2014
922611^51885-8454033Lelio R Paula01/2013
922714990^4011+4011^1499054013Hans Havermann07/2016
9228(19*2^179414+1)/754010Lelio R Paula07/2012
92293^113182-1040854002Enzo Doria02/2013
923035^34970-878653997Enzo Doria03/2013
92312^179371-163758753997Enzo Doria05/2015
923219^42225-9253996Lelio R Paula01/2013
923310190^13471-13471^1019053995Norbert Schneider05/2018
9234(3^113188+7)/7391767578453994Lelio R Paula03/2012
92357*3^113162+853993Lelio R Paula03/2014
9236(10^53991+179)/953991Serge Batalov12/2014
92382^179350-214553990Lelio R Paula10/2009
9237(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
92398^59782-6^59782-3^5978253989Mike Oakes11/2009
92403*7^63861+853970Lelio R Paula09/2014
92412^179274+7138953967Enzo Doria04/2016
92422^179259-5869553963Lelio R Paula10/2009
92436^69345+6153961Lelio R Paula10/2012
9244(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
9245(40216^11719-1)/4021553955Serge Batalov04/2015
924689*10^53951-953953Robert Price05/2017
924714^47067-353945Lelio R Paula01/2013
9248p(11700)#/2-51253937Robert Price07/2017
9249(2^179168-5)/5953934Lelio R Paula02/2012
92502^179128+841553923Lelio R Paula07/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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